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Enrico Bernardi; Antonio Bove; Vesselin Petkov
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
Journées équations aux dérivées partielles (2010), Exp. No. 4, 13 p., doi: 10.5802/jedp.61
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Résumé - Abstract

We study a class of third order hyperbolic operators $P$ in $G = \Omega \cap \lbrace 0 \le t \le T\rbrace ,\: \Omega \subset {\mathbb{R}}^{n+1}$ with triple characteristics on $t = 0$. We consider the case when the fundamental matrix of the principal symbol for $t = 0$ has a couple of non vanishing real eigenvalues and $P$ is strictly hyperbolic for $t > 0.$ We prove that $P$ is strongly hyperbolic, that is the Cauchy problem for $P + Q$ is well posed in $G$ for any lower order terms $Q$.

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